Mongo"As the example stated, if the Earth were rotating in an otherwise empty universe, would it still be considered to be rotating?"Absolutely. Just set up a Foucault's pendulum, or play pool on a frictionless table and see if your ball goes on a straight or on a curved path (we will assume somone on earth for this experiment is not on the equator). If I recall correctly, this was a problem in one of my first year of physics class.

If I'm not mistaken, "order", in reference to entropy, referrs to how basic or primordial the Universe can get. A Universe of even density, comprised entirely of hydrogen gas would be considered more orderly (less entropic) than a Universe where gravity has shaped it into galaxies, stars, etc.

Entropy would be maximum for an evenly diffused but chaotically mixing bunch of atoms. There would be transient local concentrations and emptier zones as atoms collide and zoom apart, but these would be transient and random.

(If all the atoms universe was prefectly rigidly ordered and perfectly spaced, then the atoms would be technically a solid lattice and would have lower entropy due to the ordered arrangement.)

Mike: if any of the separated atoms/particles can stick together, either chemically or gravitationally, how can the entropy already be maximized? Shouldn't there also be no more energy to liberate? Otherwise, the new compound or the new, larger object will be hotter than the things around them.

I'm assuming the atoms don't stick together, they just bounce off. If they stick, then your are going against entropy and need to have a lower energy state (delta H) to make it worthwhile...which would release heat into the environment.

Which means the maximum entropy ought to be when all the particles clump together into a single mass and that mass cools to the background temperature of the universe. (Assuming no black hole.) If there's angular momentum, I think the system can get trapped in a local minimum, where there are multiple bodies orbiting one another; entropy would be lower if they could collide, coalesce, and cool down, but there's no mechanism for them to do so.

Back to the paper, I read through it more carefully, and what he seems to be saying is that if we assume that entropy somehow (means unspecified) increases when one mass approaches another, then, given certain choice of parameters, he can derive the usual laws of gravity. He gives no clue what entropy actually means in this case. Far as I can tell, anyway.

We consider the controversial hypothesis that gravity is an entropic force that has its origin in the thermodynamics of holographic screens. Several key aspects of entropic gravity are discussed. In particular, we revisit and elaborate on our criticism of the recent claim that entropic gravity fails to explain observations involving gravitationally-bound quantum states of neutrons in the GRANIT experiment and gravitationally induced quantum interference. We argue that the analysis leading to this claim is troubled by a misinterpretation concerning the relation between the microstates of a holographic screen and the state of a particle in the emergent space, engendering inconsistencies. A point of view that could resolve the inconsistencies is presented. We expound the general idea of the aforementioned critical analysis of entropic gravity in such a consistent setting. This enables us to clarify the problem and to identify a premise whose validity will decide the faith of the criticism against entropic gravity. It is argued that in order to reach a sensible conclusion we need more detailed knowledge on entropic gravity. These arguments are relevant to any theory of emergent space, where the entropy of the microscopic system depends on the distribution of matter in the emergent space.

No surprise at all to me. Maybe now the Dark Matter theory of galactic rotation curves will finally go into the trashcan of science where it belongs, along with the Phlogiston theory of combustion and the Epicycle theory of planetary motion.

A team using the MPG/ESO 2.2-metre telescope at ESO's La Silla Observatory, along with other telescopes, has mapped the motions of more than 400 stars up to 13 000 light-years from the Sun. From this new data they have calculated the mass of material in the vicinity of the Sun, in a volume four times larger than ever considered before.

"The amount of mass that we derive matches very well with what we see — stars, dust and gas — in the region around the Sun," says team leader Christian Moni Bidin (Departamento de Astronomia, Universidad de Concepcion, Chile). "But this leaves no room for the extra material — dark matter — that we were expecting. Our calculations show that it should have shown up very clearly in our measurements. But it was just not there!"

This artist’s impression shows the Milky Way galaxy. The blue halo of material surrounding the galaxy indicates the expected distribution of the mysterious dark matter, which was first introduced by astronomers to explain the rotation properties of the galaxy and is now also an essential ingredient in current theories of the formation and evolution of galaxies. New measurements show that the amount of dark matter in a large region around the Sun is far smaller than predicted and have indicated that there is no significant dark matter at all in our neighbourhood. Credit: ESO/L. Calçada

This week, two additional studies report that even more seems to be missing (when your expectations are based on what LCDM predicts, that is). They both point at a serious lack in the amount of expected dark matter on two very different size-scales: the local universe and our immediate neighborhood within the Milky Way.

In the work titled "Missing Dark Matter in the Local Universe", Igor D. Karachentsev has looked at a sample of 11,000 galaxies in the local Universe around the MW. He has summed up the masses of individual galaxies and galaxy-groups and used this to test a very fundamental prediction of LCDM.

The idea is as simple as it is brilliant: cosmology has precise predictions as to what is the content of our universe. In particular, it predicts the density of matter to be Ωm,glob = 0.28 +- 0.03 (83 per cent of this in dark, 17 per cent in luminous matter). Now, to test this, all you have to do is to sum up all the mass within a certain volume of space, and you can estimate the actual density of mass within that volume. To be sure that your volume is representative, it needs to be large. If you only sum over, say, a sphere of 100 kpc in diameter, the density strongly depends on whether you have a galaxy in this volume or not. Karachentsev chose to use a volume of 50 Mpc around the MW. On this size-scale, the density is expected to fluctuate by only 10 percent, a reasonably low value in astronomy. The scale can thus be assumed to be representative and you should observe the mass density predicted by LCDM.

Except that you do not.

Karachentsev reports that the average mass density is only Ωm,loc = 0.08 +- 0.02, a factor of 3-4 lower than predicted and can not be explained by the uncertainties in the data or prediction. As most of the mass-content in the Universe is supposed to be dark matter, this means that most dark matter is missing in this volume.

<snip>

Indeed, a 50 page review of the observational tests of the standard model has been compiled by Pavel Kroupa in "The dark matter crisis: falsification of the current standard model of cosmology" and will appear in the Publications of the Astronomical Society of Australia (PASA-CSIRO publishing). Using a huge number of different data, Pavel Kroupa performs a strict logical falsification of the currently standard cosmological model, which is based on Einstein's theory of general relativity, concluding that cold or warm dark matter cannot exist.

Not surprising then, that the above studies have found dark matter to be missing....

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